Standard mutes:
straight - the most standard of standard. Not much variation once you put the mute in, but it could be a nice overall timbre, or something sectional. I have a few types: metal (this and this) and wood (this and this).
cup - again, fairly fixed once the mute is in. I only have this one, but it comes with an adjustable cup for little filtering adjustments.
bucket - same as others. Due to parts of Michelle's piece, I only have one type of bucket now.
practice - I have 3 different kinds: this (a metal one), this (plastic based - mine is the older, discontinued model), and this (fiber/cotton). 

Filter mutes:
plunger - 2 kinds: rubber and metal. fairly standard by this point. honestly, not my favorite thing to play with since the weight balance gets really weird, but we can work with it!
harmon - I used to have multiple types of harmon mute, but this is the only one I have now. Sonically, I totally prefer it exclusively over the others.

Nonstandard mutes:
glass plate - it's just a sheet of single-strength window-pane glass cut to my bell size. I affix it on with small binder clips. So far the only people to use this are Kurt's solo trombone piece, and the opening of Michelle's HoneyDripper.
wood plate - same with the glass, but in two types. More can totally be possible! Right now I have 1/8in thick fiberboard and 1/4in thick plywood.
plastic sheet - same but with thicker, yet bendable plastic. This could be interesting if we play around with different thicknesses of material. I could also theoretically adjust the amount of contact the sheet has with the bell with my left hand.
cardboard - same as the others, but with cardboard.
CD - just a normal CD that I can move in and out of the bell. Katie Young's piece uses this, but over a harmon mute for a kind of buzz effect. I know there's a trumpet piece by Liza Lim that also uses this extensively without an added mute.
pot lids - they work the same as the metal plunger (similar filtering/metallic buzz/etc.), but IMHO are much easier to hold and manipulate. Nick Deyoe's piece facesplitter uses it a bunch.